V2EX kernel density

Kernel Density

Definition / 释义

核密度:一种在统计学与数据分析中常用的非参数方法,用“核函数”对样本进行平滑,从而估计随机变量的概率密度函数(常见形式为“核密度估计”,KDE)。在可视化中常用于生成更平滑的分布曲线或密度图。(也可在其他语境中指“核的密度”,但最常见为统计含义。)

Pronunciation / 发音(IPA)

/knl dnsti/

Examples / 例句

Kernel density plots can reveal the shape of a distribution better than a histogram.
核密度图往往比直方图更能揭示分布的形状。

Using kernel density estimation, we smoothed the multimodal data to compare the two groups under the same bandwidth.
我们使用核密度估计对多峰数据进行平滑,并在相同带宽下比较两组差异。

Etymology / 词源

kernel 原义是“谷粒、果仁、核心”,在数学与统计中引申为“起核心作用的函数/算子”(如核函数)。density 来自拉丁语 densus(“稠密的”),在概率论中指“概率密度”。合起来的 kernel density 多指用“核(函数)”来构造/估计“密度”。

Related Words / 相关词

Notable Works / 文献与著作中的用例

  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)讨论非参数方法与密度估计相关内容
  • All of Statistics(Larry Wasserman)涵盖核密度估计等基础统计主题
  • Kernel Smoothing(M.P. Wand & M.C. Jones)系统介绍核平滑与核密度估计
  • Nonparametric Density Estimation: The L1 View(Luc Devroye & László Gyrfi)非参数密度估计经典著作
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